Abstract
We identify the two-dimensional surfaces corresponding to certain solutions of the Liouville equation of importance for mathematical physics, the nontopological Chern-Simons (or Jackiw-Pi) vortex solutions, characterized by an integer N >= 1. Such surfaces, that we call S-2 (N), have positive constant Gaussian curvature, K, but are spheres only when N = 1.
They have edges, and, for any fixed K, have maximal radius c that we find here to be c = N/root K. If such surfaces are constructed in a laboratory by using graphene (or any other Dirac material), our findings could be of interest to realize table-top Dirac massless excitations on nontrivial backgrounds.
We also briefly discuss the type of threedimensional spacetimes obtained as the product S-2(N) x R.